First, we model the power grid as a network of (virtual) synchronous machines [1]}. A simple dynamical description for such a network applies the swing equation [2]}, [3]}, which gives the dynamics of the voltage phase angle \(\theta _{i}\left(t\right)\)  and the angular velocity
\(\omega _{i}\left(t\right)\)  at each node \(i\in \left\lbrace  1,...,N\right\rbrace  \)  as
\(\frac{\text{d}}{\text{d}t}\theta _{i} & = & \omega _{i},\\M_{i}\frac{\text{d}}{\text{d}t}\omega _{i} & = & P_{i}+\Gamma _i(t)-D_{i}\omega _{i}+\sum _{j=1}^{N}K_{ij}\sin \left(\theta _{j}-\theta _{i}\right),\nonumber \) 
